Problem: Solve for $x$ and $y$ using substitution. ${x-4y = 6}$ ${y = 5x-11}$
Explanation: Since $y$ has already been solved for, substitute $5x-11$ for $y$ in the first equation. ${x - 4}{(5x-11)}{= 6}$ Simplify and solve for $x$ $x-20x + 44 = 6$ $-19x+44 = 6$ $-19x+44{-44} = 6{-44}$ $-19x = -38$ $\dfrac{-19x}{{-19}} = \dfrac{-38}{{-19}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 5x-11}\thinspace$ to find $y$ ${y = 5}{(2)}{ - 11}$ $y = 10 - 11$ $y = -1$ You can also plug ${x = 2}$ into $\thinspace {x-4y = 6}\thinspace$ and get the same answer for $y$ : ${(2)}{ - 4y = 6}$ ${y = -1}$